If the observer is very far away from the de-Sitter horizon then [1]}, \(d(a_2^+,a_2^-) \equiv d(b_2^+,b_2^-) \equiv d(a_2^{\pm },b_2^{\mp }) \gg d(a_2^{\pm },b_2^{\pm })\) , so REF  simplifies to
\(S_{\rm matter}^{\rm CEH}({\cal R}\cup {\cal I}) = \frac{Q}{6} \log \left(d^2(a_2^+,b_2^+)\right)\) 
